to provide a brief history of mathematics, and discuss the extent of its use, including some specific applications in business and technology today. Choose applications that have not yet been posted.
George Boole (1815-1864) was interested in quantifying logical problems, and created a whole branch of mathematics (Boolean Algebra) as a result. Among his publications are The Mathematical Analysis of Logic in 1847, and An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities in 1854. He specifically was interested in the operations of Binary processes; his work remained only mathematical theories until electical logic circuits were built in the late 1800's, which were the forerunners of hardware that eventually enabled the Computer Revolution.
I guess an application of math that hasn't been posted yet is that in the stock market. Stock traders use math extensively to identify price patterns that are used to buy shares for small durations of time. Neural networks try to understand price patterns and predict the future price if a particular pattern is noticed. In a way it is trying to understand human psychology at play in the stock market and make profits using it.
As a teacher, many students question the likelihood of using the things which they are taught in the "real world." Mathematics is a subject that extends throughout one's life. In daily life, math is used to balance checkbooks, measure ingredients for meals, and paying for items people need (paying and making sure they receive the correct change), as well as many other things. Outside of that, some people simply do not think about the many uses of math outside of education. While there are far too many to name, math is something which people simply dismiss when studying , but realize the importance when they failed to pay attention in class and cannot figure out simple problems.
You might like to think about the cross over between disciplines such as economics and business and mathematics. Clearly, the tool of mathematics in providing us with a system of quantifying aspects of business such as input, output and profit, becomes particularly valuable in terms of business planning and strategy.
Math has an almost unlimited amount of applications in business. From calculating compounding interest to doing efficiency analyses to simply doing the payroll, calculus, algebra, statistics, and simple arithmetic are at the heart of what even the smallest businesses do. Profits, and ultimately survival, depend on good accounting. Much of it is automated now, but it is no less important.
If this counts as business, calculus is used a great deal in economics. People use calculus, for example, to try to determine the quantity of some good or service that a firm should produce if it wishes to make the maximum possible profit.